Geology Reference
In-Depth Information
Fig. 8.4 P wave and S
wave velocity as a function
of depth. Values are plotted
from the PREM seismic
model of the Earth
(Dziewonski and Anderson
1981 ). CMB is the
core-mantle boundary, ICB
is the inner core boundary
0
2000
4000
6000
8000
10000
12000
[kg m -3 ]
14000
r
0
1000
2000
CMB
3000
4000
ICB
5000
6000
Depth
[km]
7000
Fig. 8.5 Rock density as a function of depth. Values are plotted from the PREM seismic model of the Earth
(Dziewonski and Anderson 1981 ). CMB is the core-mantle boundary, ICB is the inner core boundary
An important class of solutions to the plane
waves Eq. ( 8.12 ) is represented by periodic func-
tions having the form:
the spatial distribution of the monochromatic
wave:
¨ 2
' 2 0 D 0
2 0 C
r
(8.31)
.r;t/ D 0 .r/ cos.¨t C ª/
(8.30)
This is a scalar Helmholtz's equation, similar
to that encountered in Sect. 4.8. We know that
the solutions to this equation are combinations of
sines and cosines:
where ª is the phase , ¨ is the angular frequency,
and D ¨/2  is the wave frequency. Solutions
of the form ( 8.30 ) are called monochromatic
waves .
Substituting
( 8.30 )into 8.12 )gives
0 .r/ D e i kr
(8.32)
a
time-independent
equation
that
determines
 
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